Use a Computer Algebra System to Compute the Flux of F

question 44

Multiple Choice

Use a computer algebra system to compute the flux of F across S. S is the surface of the cube cut from the first octant by the planes $x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 }$ $\mathbf { F } ( x , y , z ) = 3 \sin x \cos ^ { 2 } y \mathbf { i } + 3 \sin ^ { 3 } z \cos ^ { 4 } z \mathbf { j } + 3 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }$

• A) 3
• B) 4
• C) \(6\)
• D) 0.67
• E) 1

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Definitions:

Equation

An equation is a mathematical statement that asserts the equality of two expressions, represented by the symbol "=".

Graph

A visual representation of data or a mathematical function using a coordinate system.

Center

The middle point of a shape or object, often an important concept in geometry and physics.

Hyperbola

A type of smooth curve lying in a plane, formed by intersecting a cone with a plane in a manner that produces a curve with two branches, each mirroring the other.